Riesz summability of spectral expansions for a class of integral operators (Q1603165)

Let \(A\) be the operator \(An(x)= \int^1_0A(x,t) u(t)dt\), \(n\in C[0,1]\). Set \(R_\lambda= (id-\lambda A)^{-1}A\). Conditions on \(A(x,t)\) and on a function \(g(\lambda,r)\) are given (in both cases rather technical ones) such that \[ -{1\over 2\pi i}\int_{|\lambda |=r} g(\lambda,r)R_\lambda f(x)d \lambda \] converges uniformly to \(f\).